Using separation of variables, it is found that the expression for the mass, M, at any time t, is given by:
![M(t) = 150e^{-kt}](https://tex.z-dn.net/?f=M%28t%29%20%3D%20150e%5E%7B-kt%7D)
<h3>What is separation of variables?</h3>
In separation of variables, supposing a differential equation in the format
, we place all the factors of y on one side of the equation with dy, all the factors of x on the other side with dx, and integrate both sides.
In this problem, the differential equation is:
![\frac{dM}{dt} = -kM](https://tex.z-dn.net/?f=%5Cfrac%7BdM%7D%7Bdt%7D%20%3D%20-kM)
Then, applying separation of variables:
![\frac{dM}{M} = -k dt](https://tex.z-dn.net/?f=%5Cfrac%7BdM%7D%7BM%7D%20%3D%20-k%20dt)
![\int \frac{dM}{M} = \int -k dt](https://tex.z-dn.net/?f=%5Cint%20%5Cfrac%7BdM%7D%7BM%7D%20%3D%20%5Cint%20-k%20dt)
![\ln{M} = -kt + C](https://tex.z-dn.net/?f=%5Cln%7BM%7D%20%3D%20-kt%20%2B%20C)
![M(t) = M(0)e^{-kt}](https://tex.z-dn.net/?f=M%28t%29%20%3D%20M%280%29e%5E%7B-kt%7D)
The initial mass is of M(0) = 150, hence:
![M(t) = 150e^{-kt}](https://tex.z-dn.net/?f=M%28t%29%20%3D%20150e%5E%7B-kt%7D)
More can be learned about separation of variables at brainly.com/question/14318343